共查询到20条相似文献,搜索用时 15 毫秒
1.
Hiroyuki Chihara 《Integral Equations and Operator Theory》2009,63(3):321-335
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex
n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain
the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order
three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat
flow determined by the phase function of the Bargmann transform.
Supported by the JSPS Grant-in-Aid for Scientific Research #20540151. 相似文献
2.
Benedetto Scimemi 《Milan Journal of Mathematics》2007,75(1):333-356
Generalizing the classical geometry of the triangle in the Euclidean plane E, we define a central point of an n-gon as a symmetric function E
n
→ E which commutes with all similarities. We first review various geometrical characterizations of some well-known central points
of the quadrangle (n = 4) and show how a look at their mutual positions produces a morphologic classification (cyclic, trapezoidal, orthogonal
etc.). From a basis of four central points, full information on the quadrangle can be retrieved. This generalizes a problem first faced by Euler
for the triangle. Reconstructing a quadrangle from its central points is a geometric analogue of solving an algebraic equation of degree 4: here the diagonal triangle plays the role of a Lagrange resolvent and the determination of loci for the central points replaces the examination of discriminants for real roots.
Received: March 2007 相似文献
3.
Let J
α
k
be a real power of the integration operator J
k
defined on the Sobolev space W
k
p
[0, 1]. We investigate the spectral properties of the operator defined on . Namely, we describe the commutant {A
k
}′, the double commutant and the algebra Alg
A
k
. Moreover, we describe the lattices Lat
A
k
and HypLat
A
k
of invariant and hyperinvariant subspaces of A
k
, respectively. We also calculate the spectral multiplicity of A
k
and describe the set Cyc
A
k
of its cyclic subspaces. In passing, we present a simple counterexample for the implication
to be valid.
相似文献
4.
Trieu Le 《Integral Equations and Operator Theory》2009,63(4):547-555
For any α > −1, let A2α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|2)α. We show that if all except possibly one of the Toeplitz operators are diagonal with respect to the standard orthonormal basis of A2α and has finite rank, then one of the functions must be the zero function.
相似文献
5.
Some Physics Questions in Hyperbolic Complex Space 总被引:1,自引:0,他引:1
In hyperbolic complex space, the Clifford algebra is isomorphic to that of a corresponding Minkowski geometry. We define the
hyperbolic imaginary unit j (j2 = 1, j ≠ ± 1, j* = − j) to generate a class of Clifford algebras. We can introduce a class of non-Euclidean spaces and discuss the general form
of 4-dimensional Lorentz transformation, and related special relativistic physics. 相似文献
6.
S. P. Eveson 《Integral Equations and Operator Theory》2008,62(4):585-589
We show that if V
α (α > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L
2(0, 1) which commutes with V , then TV
α is not supercyclic on L
2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used
by Gallardo-Gutiérrez and Montes-Rodríguez to show that V is not supercyclic. 相似文献
7.
This paper studies the connection between an analytic function φ on the unit disk and a certain type of operators induced by φ on weighted Bergman spaces A
α of analytic functions on . The general theme is the interplay between smoothness conditions on φ and the S
p
-norms of the operators induced by φ.
相似文献
8.
David Eelbode 《Advances in Applied Clifford Algebras》2007,17(4):635-649
We introduce a framework for studying differential operators which are invariant with respect to the real (complex) symplectic
Lie algebra
(
), associated to a quaternionic structure on a vector space
. To do so, these algebras are realized within the orthogonal Lie algebra
. This leads in a natural way to a refinement of the recently introduced notion of complex Hermitean Clifford analysis, in
which four variations of the classical Dirac operator play a dominant role.
David Eelbode: Postdoctoral fellow supported by the F.W.O. Vlaanderen (Belgium). 相似文献
9.
The exact bounds are obtained for the norm of the singular integral operator S on the family of rays originating at the same point. These bounds, with the use of the localization technique, are then extended
to the essential norm of S on piecewise smooth curves with finitely many points of self intersection.
Submitted: April 13, 2007. Accepted: September 19, 2007. 相似文献
10.
Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
11.
John David Herron 《Integral Equations and Operator Theory》2009,64(2):193-201
We show that the spectral radius algebras of certain quadratic operators possess nontrivial invariant subspaces. Additionally,
such algebras properly contain the operator’s commutant, so that the invariant subspaces are in some sense beyond hyperinvariant.
The spectral radius algebras of idempotents are completely described and, as a consequence, it is shown that every intransitive
collection of operators must be contained in a norm-closed proper spectral radius algebra.
相似文献
12.
13.
We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra
trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions
of that kind in integral form we admit in this paper ‘singular’ trace and Green operators. In contrast to standard conditions
in the theory of elliptic boundary value problems (like Dirichlet or Neumann conditions) our singular trace conditions, in
general, do not act on functions that are smooth up to the boundary, but admit a more general asymptotic structure. Their
action is now associated with the Laurent coefficients of the meromorphic Mellin transforms of functions with respect to the
half-axis variable, the distance to the edge. 相似文献
14.
We give a review of the analysis behind several examples of Dirac-type operators over manifolds arising in Clifford analysis.
These include the Atiyah-Singer-Dirac operator acting on sections of a spin bundle over a spin manifold. It also includes
several Dirac operators arising over conformally flat spin manifolds including hyperbolic space. Links to classical harmonic
analysis are pointed out.
Received: June 2007 相似文献
15.
Thomas A. Willging 《Archiv der Mathematik》2008,91(4):323-329
In this work we discuss Schmutz’s conjecture that in dimension 2 to 8 the distinct norms that occur in the lattices with the
best known sphere packings are strictly greater than those in any other lattice of the same covolume. We see that the ternary
conjecture is not true. However, it seems that there is but one exception: one lattice, where for one length the conjecture
fails.
Received: 11 February 2008, Revised: 20 May 2008 相似文献
16.
Viorel Catană 《Integral Equations and Operator Theory》2008,62(3):351-363
We define two-wavelet localization operators in the setting of homogeneous spaces. We prove that they are in the trace class
S
1 and give a trace formula for them. Then we show that two-wavelet operators on locally compact and Hausdorff groups endowed
with unitary and square-integrable representations, general Daubechies operators and two-wavelet multipliers can be seen as
two-wavelet localization operators on appropriate homogeneous spaces. Thus we give a unifying view concerning the three classes
of linear operators. We also show that two-wavelet localization operators on , considered as a homogeneous space, under the action of the affine group U are two-wavelet multipliers
相似文献
17.
Let (X, ~) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ~) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l
p
(X) or c_0(X), where (X, ~) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary
and sufficient results obtained in [39] in the special case and in [42] in case X = G is a general finitely generated discrete group.
Submitted: May 21, 2007. Revised: September 25, 2007. Accepted: November 5, 2007. 相似文献
18.
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based
on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these
conjectures.
Received: 11 April 2008 相似文献
19.
Let b be a BMO function, and the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator and for the pairs of weights of the type (w, ), where w is any weight and is a suitable one-sided maximal operator. We also prove that, for weights, the operator is controlled in the L
p
(w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated
k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide
a different way to obtain known results about the operators . The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral
This research has been partially supported by Spanish goverment Grant MTM2005-8350-C03-02. The first author was also supported
by CONICET, ANPCyT and CAI+D-UNL. The second author was also supported by Junta de Andalucía Grant FQM 354. 相似文献
20.
A geometric procedure is used to isolate four Bernoulli integrals for a nonlinear, two-dimensional magnetohydrodynamic system.
The general solution of the latter may thereby be constructed. 相似文献